$\begin{equation*} \begin{cases} 2x + y = 12 &\\ 7x - 2y = 31 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 12 - 2x &\\ 7x - 2y = 31 & \end{cases} \end{equation*}$
7x − 2(12 − 2x) = 31
7x − 24 + 4x = 31
11x = 31 + 24
11x = 55
x = 5
y = 12 − 2 * 5 = 12 − 10 = 2
Ответ: x = 5, y = 2.

$\begin{equation*} \begin{cases} y - 2x = 4 &\\ 7x - y = 1& \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 2x + 4 &\\ 7x - y = 1& \end{cases} \end{equation*}$
7x − (2x + 4) = 1
7x − 2x − 4 = 1
5x = 1 + 4
5x = 5
x = 1
y = 2 * 1 + 4 = 2 + 4 = 6
Ответ: x = 1, y = 6.

$\begin{equation*} \begin{cases} 8y - x = 4 &\\ 2x - 21y = 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = 8y - 4 &\\ 2x - 21y = 2 & \end{cases} \end{equation*}$
2(8y − 4) − 21y = 2
16y − 8 − 21y = 2
−5y = 2 + 8
−5y = 10
y = −2
x = 8 * (−2) − 4 = −16 − 4 = −20
Ответ: x = −20, y = −2.

$\begin{equation*} \begin{cases} 2x = y + 0,5 &\\ 3x - 5y = 12& \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 2x - 0,5 &\\ 3x - 5y = 12& \end{cases} \end{equation*}$
3x − 5(2x − 0,5) = 12
3x − 10x + 2,5 = 12
−7x = 12 − 2,5
−7x = 9,5
$x = -\frac{9,5}{7} = -\frac{95}{70} = -\frac{19}{14} = -1\frac{5}{14}$
$y = 2 * (-\frac{19}{14}) - \frac{1}{2} = -\frac{38}{14} - \frac{7}{14} = -\frac{45}{14} = -3\frac{3}{14}$
Ответ: $x = -1\frac{5}{14}, y = -3\frac{3}{14}$.